Method of heat exchange with high viscosity liquids



Aug. 27, 1968 J. w. SMITH ETAL 3,398,784

METHOD OF HEAT EXCHANGE WITH HIGH VISCOSITY LIQUIDS Filed Sept. 12, 1966 3 Sheets-Sheet l LEGEND Q .060 Y O SMOOTH 0.026 0 0.060

Aug. 27, 1968 Filed Sept. 12, 1966 J. W. SMITH ETAL METHOD OF HEAT EXCHANGE WITH HIGH VISCOSITY LIQUIDS Sheets-Sheet 2 LEGEND 0V0 I. O SMOOTH 0 0.060 "CON f 0 0 I 9. I.

1/ 0" d// f I I J WATER 7, 1968 J. w. SMITH ETAL 3,398,784

METHOD OF HEAT EXCHANGE WITH HIGH VISCOSITY LIQUIDS Filed Sept. 12, 1966 3 Sheets-Sheet LEGEND 5 0 0 SMOOTH moo 2 a 4 s 6 7 a 9 10.000

United States Patent 3,398,784 METHOD OF HEAT EXCHANGE WITH HIGH VISCOSITY LIQUIDS James W. Smith, Leaside, Ontario, and Robert A. Gowen, Toronto, Ontario, Canada, assignors to The Electric Reduction Company of Canada, Ltd., Toronto, Ontario, Canada 7 Filed Sept. 12, 1966, Ser. No. 578,675 Claims priority, application Great Britain, Sept. 13, 1965, 38,9 62/ 65 9 Claims. (Cl. 1651) ABSTRACT OF THE DISCLOSURE A method of effecting heat exchange with a liquid having a Prandtl number of at least 30, e.g., polyalkylene glycol, in which the liquid is passed under conditions of non-laminar flow, i.e., in the region between laminar and fully turbulent flow, through hydrodynamically rough heat exchange channels.

The present invention relates to a method of heat exchange using high viscosity liquids.

It is known to pass liquids or gases through heat exchanging tubes having hydrodynamically rough or smooth surfaces for effecting heat exchange between said liquids or gases. It is further known that when the liquids fiow through rough tubes under conditions of non-laminar flow the heat transferred between the liquids and the tubes is significantly increased, i.e., the heat transfer coefiicient of rough tubes is higher than that of smooth tubes under the same conditions, of non-laminar flow. However although with the hydrodynamically rough tubes the heat transfer is significantly better, the pressure drop along the tube and as such the power loss in passing the liquid along the tube is also substantially increased and this is presumed to be due to the increased friction between the liquid and the rough walls of the tube. In fact the heat transfer efficiency namely the ratio of the rate of heat transfer between the liquid and the internal walls of the tube and the pressure drop or power loss in passing the liquid along the tube is lower with hydrodynamically rough tubes as compared with hydrodynamically smooth tubes and as such hydrodynamically rough tubes have not received commercial acceptance in heat exchangers.

It has now been found however that the heat transfer efiiciency is dependent upon the Prandtl number of the liquid being used and whereas heretofore only liquids of low Prandtl number not greater than 8 and hence normally of low viscosity have heretofore been tested, with high viscosity liquids having a high Prandtl number such as those having a Prandtl number of at least 30 the heat transfer etficiency with non-laminar flow is substantially greater with hydrodynamically rough tubes than with smooth tubes. This renders the use of rough tubes in heat exchangers, in which the liquid has a high Prandtl number commercially attractive. The Prandtl number of a liquid is dependent on the viscosity of the liquid and is equal to Cp /K where C,, is the specific heat at constant pressure of the liquid, K is the thermal conductivity of the liquid and ,u is the absolute viscosity.

According to the present invention therefore there is provided a method of effecting heat exchange with a liquid having a high Prandtl number and hence normally a high viscosity which comprises passing said liquid under conditions of non-laminar flow through the tubes of a heat exchanger, the internal surfaces of said tubes being hydrodynamically rough.

As aforesaid in order to achieve the benefits of the present invention the liquid must have a high Prandtl number and hence for most liquids a high viscosity and whereas with low viscosity liquids the heat transfer efficiency is lower with non-laminar flow for tubes having hydrodynamically rough internal surfaces than for those with smooth internal surfaces applicants have found that the heat transfer efiiciency is somewhat proportional to the viscosity of the liquid as indicated by the Prandtl number and at a Prandtl number of about 30 the heat transfer efiiciency for non-laminar flow becomes higher for tubes with hydrodynamically rough internal surfaces than for those with smooth internal surfaces. Desirably the Prandtl number of the heat exchange liquid is of the order of hundreds and generally the higher the Prandtl number the higher the heat transfer efiiciency. A particular heat exchange liquid which may be mentioned is a polyalkylene glycol supplied under the trade name Ucon which has a Prandtl number of 349 at a temperature of 86 F.

It is critical in order to achieve the benefits of the present invention that the flow of liquid through the tubes or pipes is non-laminar and whereas the benefits are achieved anywhere in turbulent flow a better heat exchange is achieved and better heat transfer efficiency is achieved in the flow regime between laminar and fully turbulent flow. In this direction the Reynolds number which is a measure of conditions of flow and is equal to VD where V is the mean velocity of the liquid, p is the density of the liquid, ,u is the viscosity of the liquid and D is the diameter of the tube is at least 2,500 and preferably 2,500 to 10,000. An optimum heat transfer efliciency is usually achieved when the Reynolds number is of the order of 2,500 and 4,000, preferably 2,750 to 3,500 and optimally 2,750 to 3,000.

To achieve the benefits of the present invention it is essential that the internal surfaces of the tube must be hydrodynamicaly rough and equivalent sand roughness of at least 0.026 up to 0.60 and higher have been found suitable. Equivalent sand roughness (e /D) has become a standard method of calibrating the roughness of the internal surface of a tube or pipe and is obtained for any particular tube, by comparing the plot of friction factor (as hereinafter defined) against Reynolds number for liquid flowing through the tube with similar plots obtained with tubes having their internal surfaces roughened by gluing sand particles of diameter e to the internal surface of the tube of diameter D, these latter plots being referred to as Fanning or Moody plots. Thus tube having a Fanning or Moody plot which is substantially identical to the plot obtained with the roughened tube constitutes a tube of equivalent sand roughness and it will be readily realized that the equivalent sand roughness is not the same as the actual roughness of the pipe.

The present invention will be further illustrated by way of the following example in which the results are given in graphs shown in the accompanying drawings in which:

FIGURE 1 is a plot of friction factor against Reynolds 'number for three pipes using Ucon as the liquid;

EXAMPLE Three brass pipes were used each having a length of 12 inches and an internal diameter of inch; one of the pipes being hydrodynamically smooth and used for comparative purposes and the other two being roughened to a different equivalent sand roughness by internally threading with specially made taps. Each pipe was externally thermally insulated and heated electrically, the heat input to the pipe being determined from the readings of a voltmeter and ammeter in the electrical circuit and the wall temperature of the pipe being determined from four thermo-couples embedded in the pipe, the temperature reading being recorded continuously on a strip chart potentiometer. The pressure drop through each pipe was measured by means of a differential manometer and the liquid velocity through the pipe was measured with a rotameter. The liquids tested were (a) that supplied under the trademark Ucon which as aforesaid is a polyalkylene glycol of high viscosity having a Prandtl number of 349 and for comparison purposes (b) water which is a low viscosity liquid having a Prandtl number below 8.

Non-heating runs were first conducted at room temperature and the velocity of the liquid, the pressure drop and the density of the liquid were measured. From these measurements the friction factor f was calculated from the equation f p)gc 2V pL wherein A is the pressure drop along the pipe; L is the length of the pipe; D is the diameter of the pipe; V is the velocity of the liquid through the pipe; p is the density of the liquid and g is the dimensional constant equal to 4.l7 10 (1b.) (ft.)/(hr.) (lb. force). Further the Reynolds number was calculated from the equation DV N Re IL P where D, V and p are as above and ,u is the viscosity of the liquid.

A plot of the friction factor against Reynolds number was made as shown on FIGURE 1 for Ucon and as the plot for the smooth tube followed the accepted curve this supports the assumption that Ucon is completely Newtonian. The roughened tube plots were compared with the conventional Fanning or Moody plots for internally sand roughened tubes and the equivalent sand roughness for the tubes as is shown in the graph were found to be 0.026 and 0.60 respectively.

Heat was then supplied to the tubes from the electrical circuit. Ucon and water were then passed through the tube and the wall temperature of the tubes measured from the thermo-couples embedded therein. The inlet and outlet temperature of the liquid passing through the tubes was also measured by means of thermometers and the rate of heat supplied to the pipe obtained from the wattage supplied through the electrical circuit.

From the rate of heat supplied to the tube the heat flux (q) i.e., the rate of heat flow from the tube to the liquid was readily determined and the heat transfer coeflicient (h) calculated from the equation where a is the interfacial area of the internal surface of the tube and the liquid and AT is the mean temperature difference between the temperature of the wall and the bulk temperature of the fluid. In this example AT remains constant along the whole length of the tube. From the heat transfer coefficient the Nusselt number N which is a dimensionless factor conventionally used in fluid mechanics is calculated from the equation where D and h are as aforesaid and K is the thermal conductivity of the liquid. It will be readily realized that the Nusselt number is a measure of heat transfer from the wail of the tube to the liquid.

A plot of Nusselt number against Reynolds number is shown in FIGURE 2 and this readily illustrates that for non-laminar flow particularly turbulent flow of the liquid the heat transfer for internally roughened pipes is substantially higher than for internally smooth pipes.

Finally as will be seen from FIGURE 3 a plot was made of the dimensionless group against Reynolds number the Stanton Number N being calculated from the equation where V is the velocity of the liquid C is the specific heat of the liquid, p is the density of the liquid and h is as above. As will be readily seen from the equations the dimensionless group plotted against the Reynolds number is a measure of the heat transfer efiiciency i.e., the heat transmission per unit pressure drop along the tube as the friction factor 1 contains the pressure gradient A i/L and h is the heat transfer coefficient. The Reynolds number is introduced into the grouping to account for variation in the tube size.

From a consideration of FIGURE 3 it will be seen that the heat transfer efiiciency, i.e., the dimensionless grouping, with Ucon is substantially higher with tubes having internally roughened surfaces than with tubes having internally smooth surfaces for non-laminar and particularly turbulent flow whereas with water the reverse is the case. This difference in behavior holds regardless of whether the true surface area of effective smooth surface is used to calculate the heat transfer coefiicient and whereas the increase in surface area for the roughest tube does not normally exceed 28% the increase in the heat transfer efiiciency over the smooth tube is never less, insofar as has ben ascertained experimentally, than 200% What we claim as our invention is:

1. A method of effecting heat exchange with a liquid having a Prandtl number of at least 30 which comprises passing said liquid under conditions of non-laminar flow through the heat exchange channels of the heat exchanger, the internal surfaces of said channels being hydrodynamically rough.

2. A method as claimed in claim 1 in which the liquid has a Pnandtl number of at least 100.

3. A process as claimed in claim 1 in which the liquid is a polyalkylene glycol.

4. A method as claim in claim 1 in which the channels are in the form of tubes.

5. A method as claimed in claim 1 in which the flow 3f the liquid is in the range laminar to fully turbulent 6. A method as claimed in claim 1 in which the flow of the liquid through the heat exchanger is such to achieve 21 Reynolds number in the range 2,500 to 4,000.

7. A method as claimed in claim 1 in which the flow of the liquid through the heat exchanger is sufiicient to provide a Reynolds number in the range 2,750 to 3,500.

8. A method as claimed in claim 1 in which the flow of liquid through the heat exchanger is sufficient to provide a Reynolds number of 2,750 to 3,000.

9. A method as claimed in claim 1 in which the hydrodynamically rough surfaces have an equivalent sand roughness of 0.026 to 0.60.

References Cited UNITED STATES PATENTS 2,279,548 4/ 1942 Bailey -179 2,426,044 8/1947 OBrien 165133 3,088,494 5/1963 Koch et al. l65 l33 ROBERT A. 0LEARY, Primary Examiner. CHARLES SUKALO, Asistant Examiner. 

